In known manner, a pump generally includes a pump body in which a piston is mounted to slide between a rest position and a dispensing position for dispensing the fluid contained in the pump, in particular in a pump chamber. An abutment member is generally fitted into the top edge of the pump body to define the rest position of the piston. This abutment member may, for example, be in the form of a ferrule that co-operates with the piston when said piston is in the rest position. Usually, the piston is provided with a bottom sealing lip and with a top sealing lip, the top sealing lip providing sealing between the piston and the pump body. The sealing between the piston and the ferrule is generally provided at radial contact surfaces between a bottom radial edge of the ferrule and a corresponding radial surface of the piston. That configuration can suffer from drawbacks. Firstly, the sealing between the piston and the ferrule is not good because it is not provided by means of a deformable flexible portion such as a sealing lip, as it is with the pump body. Secondly, in order to guarantee good leaktightness between the ferrule and the piston, it is necessary, when the piston is in the rest position, to have a relatively large force exerted by the return spring of the pump to enable the radial contact surfaces of the ferrule and of the piston to provide sufficient leaktightness. A relatively high force when the pump is in the rest position requires a large force to actuate the pump because the return spring cannot be completely relaxed in the rest position. In addition, since the abutment position is defined by the point of sealing between the ferrule and the piston, the manufacturing tolerances of the various components mean that the abutment position is not constant, but rather that it can vary as a function of said manufacturing tolerances. Modifying, even slightly, the rest position of the pump can have consequences on the metering of the fluid when the pump is actuated.